now that's what i call phÂœnix 58

Mattb · Post by **Mattb** » Wed Oct 24, 2007 10:01 am

Mont Blanc is the most famous and obvious one to go for....but its wrong

Cardinal Sin · Post by **Cardinal Sin** » Wed Oct 24, 2007 10:09 am

Bah. I know it starts with an E and it's in Russia but that's as much as I can remember.

harry 3 · Post by **harry 3** » Wed Oct 24, 2007 2:09 pm

How about 40, 30,30,0,0. Would get at least three votes.

Cardinal Sin · Post by **Cardinal Sin** » Wed Oct 24, 2007 2:26 pm

Not necessarily. Remember that the pirates wants as much gold as possible and each pirate is capable of rational thought (i.e. they realise that if the motion is rejected, it will be Pirate B's turn to make a proposal and the implications of this).

Therefore, Pirate B could veto the motion cos then it would be his proposal, and he could allocate more gold to himself.

It is easier if you work backwards, i.e. what would be the proposal if it was just Pirate E, or just pirates E and D etc...

Istenem · Post by **Istenem** » Wed Oct 24, 2007 3:21 pm

i wish i was better at things like this but i'm a bit of a dolt.

working backwards i came up with:

D51 E49 (approved 2-0)
C51 D49 E0 (approved 2-1)
B51 C49 D0 E0 (2-2 casting vote = approval)
A35 B34 C33 D0 E0 (approved 3-2)

any good?

Cardinal Sin · Post by **Cardinal Sin** » Wed Oct 24, 2007 3:24 pm

The distribution is rather more unfair than that.

Since the proposer receives the casting vote, if it were down to the last 2 pirates, it would be

D: 100, E: 0

You can take it from there!

(and I don't mean to hurry you, but I've been waiting for the last 2.5 hours waiting for you to take your fecking Scrabulous shot)

Istenem · Post by **Istenem** » Thu Oct 25, 2007 12:17 pm

i just cheated

ops: but i'm very impressed with the answer and the logic behind it

theoak · Post by **theoak** » Thu Oct 25, 2007 12:25 pm

ok, im gonna go:

cde; 66,34,0
bcde; 75,25,0,0
abcde; 60,20,20,0,0

??

theoak · Post by **theoak** » Thu Oct 25, 2007 12:27 pm

this assumes each of the 'lesser' pirates getting AN amount of money will be happy with what WOULD be the average amount were the money split equally?

theoak · Post by **theoak** » Thu Oct 25, 2007 12:30 pm

actually, that sucks I guess cos if only offered an even share; they will veto.

harry 3 · Post by **harry 3** » Thu Oct 25, 2007 12:37 pm

Surely in the first stage the allocation is irrelevant as c d e will vote to throw a overboard !

theoak · Post by **theoak** » Thu Oct 25, 2007 12:40 pm

I should have been less hurried and read the quesiton properly, didnt realise pirate get killed if their choice is denied!

Cardinal Sin · Post by **Cardinal Sin** » Thu Oct 25, 2007 12:47 pm

®© harry2½ wrote:Surely in the first stage the allocation is irrelevant as c d e will vote to throw a overboard !

Nope. Because if they all conspire to throw A off, then they could end up with less gold than he might offer them.

The distribution if there were 2 pirates left:

D: 100, E: 0 : D knows that he gets the casting vote so he can have all the gold.

Therefore, if there are 3 left

C knows that all he has to do is offer E 1 piece of gold to be sure of his vote (because it is still 1 more gold than he would get if he rejected the proposition).

This means that with 3 pirates left it would be:

C: 99, D:0, E:1

Anyone want to try the next step?

theoak · Post by **theoak** » Thu Oct 25, 2007 1:49 pm

my brain hurts now. 98,0,0,1,1 would work then?

Cardinal Sin · Post by **Cardinal Sin** » Thu Oct 25, 2007 2:07 pm

Close enough. (and it might actually work. My brain hurts too).

The answer on my card is A: 98 coins B: 0 coins C: 1 coin D: 0 coins E: 1 coin

You can read more here:

http://en.wikipedia.org/wiki/Pirate_loot_problem

Over to the oaky one (even though there seems to be 2 quizzes running!)